Predicting Competitive and Non-Competitive Torquoselectivity in Ring-Opening Reactions using QTAIM and the Stress Tensor

We present a new vector-based representation of the chemical bond referred to as the bond-path frame-work set $\mathbb{B} = {p, q, r}$, where $p$, $q$ and $r$ represent three paths with corresponding eigenvector-following path lengths $\mathbb{H}^{*},\mathbb{H}$ and the bond-path length from the quantum theory of atoms in molecules (QTAIM). We find that longer path lengths $\mathbb{H}$ of the ring-opening bonds predict the preference for the transition state inward (\textbf{TSIC}) or transition state outward (\textbf{TSOC}) ring opening reactions in agreement with experiment for all five reactions \textbf{R1-R5}. Competitiveness and non-competitiveness have traditionally been considered using activation energies. The activation energy however, for \textbf{R3} does not satisfactorily determine competitiveness or provide consistent agreement with experimental yields. We choose a selection of five competitive and non-competitive reactions; methyl-cyclobutene (\textbf{R1}), ethyl-methyl-cyclobutene (\textbf{R2}), iso-propyl-methyl-cyclobutene (\textbf{R3}), ter-butyl-methyl-cyclobutene (\textbf{R4}) and phenyl-methyl-cyclobutene (R5). Therefore, in this investigation we provide a new criterion, within the QTAIM framework, to determine whether the reactions \textbf{R1-R5} are competitive or non-competitive. We that find \textbf{R2}, \textbf{R3} and \textbf{R5} are competitive and \textbf{R1} and \textbf{R4} are non-competitive reactions in contrast to the results from the activation energies, calling into question the reliability of activation energies.